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2 Fundamenta Informaticae

2 2008

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Complete Process Semantics of Petri Nets

Juhás G., Lorenz R., Mauser S.

Fundamenta Informaticae

2008

Vol. 87, nr 3-4

331-365

In the first part of this paper we extend the semantical framework proposed in [22] for process and causality semantics of Petri nets by an additional aim, firstly mentioned in the habilitation thesis [15]. The aim states that causality semantics deduced from process nets should be complete w.r.t. step semantics of a Petri net in the sense that each causality structure which is enabled w.r.t. step semantics corresponds to some process net. In the second part of this paper we examine several process semantics of different Petri net classes w.r.t. this aim. While it is well known that it is satisfied by the process semantics of place/transition Petri nets (p/t-nets), we show in particular that the process semantics of p/t-nets with weighted inhibitor arcs (PTI-nets) proposed in [22] does not satisfy the aim. We develop a modified process semantics of PTI-nets fulfilling the aim of completeness and also all remaining axioms of the semantical framework. Finally, we sketch results in literature concerning the aim of completeness for process definitions of various further Petri net classes. The paper is a revised and extended version of the conference paper [18].

Causal Semantics of Algebraic Petri Nets distinguishing Concurrency and Synchronicity

Juhás G., Lorenz R., Mauser S.

Fundamenta Informaticae

2008

Vol. 86, nr 3

255-298

In this paper, we show how to obtain causal semantics distinguishing "earlier than" and "not later than" causality between events from algebraic semantics of Petri nets. Janicki and Koutny introduced so called stratified order structures (so-structures) to describe such causal semantics. To obtain algebraic semantics, we redefine our own algebraic approach generating rewrite terms via partial operations of synchronous composition, concurrent composition and sequential composition. These terms are used to produce so-structures which define causal behavior consistent with the (operational) step semantics. For concrete Petri net classes with causal semantics derived from processes minimal so-structures obtained from rewrite terms coincide with minimal so-structures given by processes. This is demonstrated for elementary nets with inhibitor arcs.